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Definition df-ltxr 8752
 Description: Define 'less than' on the set of extended reals. Definition 12-3.1 of [Gleason] p. 173. Note that in our postulates for complex numbers, is primitive and not necessarily a relation on . (Contributed by NM, 13-Oct-2005.)
Assertion
Ref Expression
df-ltxr
Distinct variable group:   ,

Detailed syntax breakdown of Definition df-ltxr
StepHypRef Expression
1 clt 8747 . 2
2 vx . . . . . . 7
32cv 1618 . . . . . 6
4 cr 8616 . . . . . 6
53, 4wcel 1621 . . . . 5
6 vy . . . . . . 7
76cv 1618 . . . . . 6
87, 4wcel 1621 . . . . 5
9 cltrr 8621 . . . . . 6
103, 7, 9wbr 3920 . . . . 5
115, 8, 10w3a 939 . . . 4
1211, 2, 6copab 3973 . . 3
13 cmnf 8745 . . . . . . 7
1413csn 3544 . . . . . 6
154, 14cun 3076 . . . . 5
16 cpnf 8744 . . . . . 6
1716csn 3544 . . . . 5
1815, 17cxp 4578 . . . 4
1914, 4cxp 4578 . . . 4
2018, 19cun 3076 . . 3
2112, 20cun 3076 . 2
221, 21wceq 1619 1
 Colors of variables: wff set class This definition is referenced by:  ltrelxr  8766  ltxrlt  8773  ltxr  10336
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